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A Pokemon's chance of being Shiny is determined as part of it's personality values, which means this gives your answer:

>A Pokémon's personality value is an unsigned 32-bit integer that is created when the Pokémon is first encountered; it is set as soon as the Pokémon appears in the wild, the Pokémon's Egg is received from the Day Care man or another NPC, or the Pokémon itself is received from an NPC.